Delta-Sigma modulators are a class of voltage-to-frequency conversion devices. When coupled to a digital filter, the combination of the delta-sigma modulator and filter yields a delta-sigma modulator A/D converter with very high performance. A typical delta-sigma modulator functions as a voltage-to-frequency converter which produces an output voltage of +b or -b (where b is typically +1 volt) in accordance with the input voltage to the modulator. (When the input voltage is zero, the analog modulator output voltage is zero.) The digital signal produced by the delta-sigma modulator, when filtered by the digital filter, yields a serial signal representative of the level of the voltage input to the modulator.
In the past, delta-sigma modulators have been tested by comparing whether the frequency domain value of the Signal-to-Noise (S/N) ratio of the modulator is significantly below a prescribed value. The frequency domain value of the S/N ratio has been established from a power spectrum density of the samples output by the delta-sigma modulator when samples of a sinusoidal signal is applied to its input. The power density spectrum has been computed by performing a Fourier transform on each output sample to obtain its value in the frequency domain, and thereafter multiplying the value by its conjugate.
Testing the delta-sigma modulator in this fashion is a relatively complex undertaking. The complexity (i.e., number of operations) associated with performing a Fourier transform on n delta-sigma modulator output signals (where n is an integer) is n log(n) complex multiplications. The complexity associated with establishing a power spectrum density of the n output signals by multiplying the Fourier transform of each signal by its complex conjugate is 2n complex multiplications because the Fourier transform and complex conjugate of each signal are typically complex numbers. Lastly, the complexity associated with establishing the signal-to-noise ratio of the delta-sigma modulator from the power spectrum density of the samples output is approximately n real additions. Thus, the overall complexity associated with testing the delta-signal modulator in this manner is on the order of n log(n)+2n complex multiplications and n real additions.
Thus, there is a need for a technique for testing a delta-sigma modulator with reduced complexity.